An impeller for a centrifugal rotating machine, such as a centrifugal compressor, is generally composed of an approximately disk shaped main body having a front and a rear surfaces, with respect to the direction of the fluid flow, provided with a central circular hole that fits with a hub attached to a rotating axis, a shroud having a front and a rear surfaces that is arranged at an interval outward of the main body and a series of blades that couple the front surface of the main body and the rear surface of the shroud. A series of passages are formed by the front surface of the main body, the rear surface of the shroud and the side surfaces of the blades, the passages serving as a flow passage for compressing air. Generally the blades follow a curved line bending in both radial and axial direction. The front surface of the main body and the rear surface of the shroud bend accordingly to accommodate the curvature of the blades. The air flow enters the impeller tangentially to the front surface of the main body and exits from the impeller in an axial direction. A shrouded impeller may be manufactured from one single solid piece of material or it may instead be constructed from two or more components, which are attached together to form the finished product. In general the various components are fixed by welding. The impeller can be constructed from one single solid piece by full milling, but this process is very difficult and time consuming due to the limited accessibility given the complex shape of the flow passages. Electrical Discharge Machining (EDM) process is also an option for the single piece fabrication by means of electric spark metal-removal erosion. In this process an electric spark is used as the cutting tool to erode the single monolithic disc to produce the finished part to the design shape. The metal-removal process is performed by applying a pulsating (ON/OFF) electrical charge of high-frequency current through the electrode to the work piece. This technique involves the step of machining the single piece by premilling followed by EDM roughing and EDM finishing. For the reason set before, special shaped electrodes and special shaped tools must be used to conform to the complex passages design. The process is very time consuming and many working days are necessary to produce a single impeller. The impeller can be produced also by fabricating first two components i.e. by obtaining the blades by means of milling the main body or the shroud and subsequently by welding the two parts. With welding filling the internal junction between blades and main body or shroud given the lack of good accessibility is very difficult and welding defects easily occur in the fixing and thus the risk of cracking and deformation, i.e. thermal distortion, due to locally high temperatures, can become very high. Besides the surfaces of the flow passage will not have in general the smoothness required. In definitive it is very hard by using state of the art techniques to obtain an impeller with the high quality and reliability required. For these reasons a method to make an impeller having higher quality and that results in shorter production time and lower costs is highly needed.